OK, well, do all the quests except Leyawiin and Anvil first.
The last two require you to do a bit of fighting and you may get caught out if you are not strong enough.
Merlin (my latest char) is a Breton Mage, pretty standard, he got into the Arcane Uni (AU) really early, about Lv2. From there, those quests are quite tough for a newbie, so once you get your foot in the door, do other quests like the Main Quest, maybe even Arena if you have the balls, or just regular old dungeon-diving.
As you should know, most of a Mage skill set levels real quick, like Mysticism, Alteration, Conjuration, Alchemy and Illusion. You can level those by standing around your house.
Destruction and Restoration, on the other hand require nothing but bloody combat to improve decently. Oblivion gates are good for that.
Check out two thread I started here: http://www.gamesas.com/index.php?/topic/1112495-levelling-destruction-and-restoration/
And: http://www.gamesas.com/index.php?/topic/1112755-anatomy-of-a-mage/
Hope that helps you!